As an alternative to the Total Probability Theorem, the "depends" argument that students use to calculate marginal probabilities is studied. We discuss an experience with undergraduate engineering students who took a computed aided basic probability course based on the frequency approach. The result of this experience shows that an adequate interpretation of the outcomes of simulated random experiments allows conjecturing and arguing algebraic results of the theory of probability.
This paper continues earlier studies about the teaching and learning of the arithmetic average and it is part of a broader research in progress at Santiago of Compostela University (Spain). We have analyzed a sample of six teaching manuals (textbooks) used for teaching mathematics at high schools in Salvador, Bahia. The study is based on theoretical ideas by Godino and Batanero (1994; 1998) and Godino and Recio (1997) who propose a semiotics perspective based on the functions of signs by Hjelmslev (1943), later known as "semiotic function".( Eco, 1979).
In this article, we describe an experience with the teaching and learning of the Poisson´s Model, directed to university students. We used the Anthropological Theory of the Didactic and the principles of the Mathematical Modeling Process for the elaboration of the teaching sequence, showing that it is possible to build the model without resorting to the Binomial limit, making use of the notions of calculus. In the development of the learning activities, the computer was used as a didactic tool. The analysis of results was based on the Theory of the Semiotic Functions and proved that the students learned many significant elements considered in the teaching. On the other hand, the study allowed for the identification of difficulties throughout the process: for example, the interpretation of expressions such as "at least" and "at most", the representation used, the analysis of the results of hypothesis tests and the manipulation of the software.
Basic subjects play an important role in engineering education. Applied Statistics may be regarded as a basic subject as well as a technical subject, and occupies therefore a central place in agro-forestry engineer professional curriculum. Statistics is present in some proportion in our whole life. With the purpose of implementing new methods for statistical learning, in the framework of European Higher Education Area, an experimental proof has been started during a quarter of academic year 2004/05 of the third class in the Faculty of Forestry Engineers from Polytechnic University of Madrid. Methodology was oriented for students to improve capacities of oral expression, information search, use of recent technologies and experience in knowledge analysis and synthesis, together with acquisition of minimum knowledge required in the subject.
Our interest in the techno-mathematical literacies employees need in their jobs has led us to do case studies in different industrial sectors and to design learning opportunities for improving employees' techno-mathematical literacies. We conceptualise the learning opportunities not as training or transfer, but as forms of "boundary crossing" between employees from a company and us as researchers. Two examples are given in which packaging managers explore and discuss a realistic problem using TinkerPlots, an educational software tool. The results emphasise how important it is to allow managers to bring their ideas and concerns to the problem situation so they can connect these to statistical theory that is relevant in statistical process control (SPC). This approach is contrasted with SPC training we have observed in two industrial sectors.
A postgraduate teaching performance evaluation methodology is presented starting with the design of a questionnaire applied to enrolled in the Master's in Sciences program. The evaluation instrument was divided into four sections and programmed in informatics language. Regular students answered 543 questionnaires, one per course taken during 2003 and 2004. The information was studied statistically course-by-course from a point of view both educational and psychological. The results were analyzed course-by-course taught and on an overall basis.
Being able of correctly read and interpret two ways tables is a basic component of statistical literacy for every citizen. Therefore, future teachers who will be responsible to teach statistics to children at school level should acquire these abilities along their training. However, this capacity is taken for granted in Spain and its teaching is not usually included in the curriculum for training teachers. In this study present the results of a small exploratory study that describe the future teachers' semiotic conflicts in solving elementary probability problems when data re given in a two-way table.
Collaboration is an important feature of today's teacher education. According to several researchers, teachers are open to work collaboratively, although they often work in an individual and solitary manner. Since the nineties statistics education includes the need for children to be able to pose questions, collect, organize and represent data in a spirit of investigation and exploration. This is enhanced by implementing student projects. The main research question in this paper is to clarify how three pre-service math teachers planned and prepared classes and reflected afterwards upon them. A qualitative methodology was adopted. It is shown with empirical evidence that collaborative work between teachers is an important approach to solve difficulties in statistical and didactical knowledge. Our results also show that these are the areas teachers have to improve in order to become more confident teachers of Statistics.
The development of students' competencies expressed in current curricular documents is a complex task that teachers have to perform (Brocardo, 2005). Project work is a practice that can allow for this development (Abrantes, 1994). According to the Portuguese Department of Basic Education (2001), project work, namely in statistics, is one of the learning experiences that all students should have the opportunity to engage in. This study is a part of the research project Interaction and Knowledge, whose main goal is to study and implement collaborative work within classrooms. We discuss how students from two 7th grade classes (compulsory education, 12/13 years old) used project work in statistics to learn more about statistical contents, about their colleagues, and to develop social, cognitive and affective competencies.
Too often students leave their first statistics course with at best a fuzzy understanding of basic statistical concepts and procedures. A disconcertingly high proportion cannot adequately describe or perform a t-test, for example, when taking subsequent courses. This suggests that a different approach to teaching and learning is necessary, particularly for graduate students who will need statistical tools in their research. Rote memorization of facts does not provide the preparation requisite for graduate research. A constructivist approach in course design could provide a learning environment in which students move beyond lower level cognitive skill development. Initial implementation of this approach has produced encouragingly positive results.